I decided to just go through all the orange shinies, then went back and bolded any available in Sun and UM. Italicized Pokémon are borderline (details given in parenthesis)
Charmander and Charmeleon (borderline gold)
Spearow (wings are orange)
The Pikachu line (Alolan Raichu has orange ears and tail only)
Kantonian Vulpix
Vileplume (petals only)
Paras (kind of a borderline red) and Parasect
Kantonian Geodude
Shellder
The Exeggcute line
Goldeen (borderline gold) and Seaking
Electabuzz and Electivire
Magikarp (borderline gold)
Flareon
Zapdos (borderline gold)
Moltres (flames only)
Chikorita and Bayleef (borderline brown)
The Cyndaquil line
The Ledyba line (borderline gold)
Sunkern (borderline gold)
Girafarig
The Pineco line (borderline gold)
Magby
Raikou
Ho-Oh
Torchic and Combusken (and Mega Blaziken to an extent)
The Zigzagoon line
Ludicolo (borderline brown)
The Taillow line (head and chest only)
The Shroomish line
Makuhita
Vibrava and Flygon (wings and eyes only for Flygon)
The Cacnea line
Solrock (borderline red)
Crawdaunt
Latias
The Kricketot line (borderline gold)
The Shinx line (borderline gold)
The Combee line
Uxie
The Tepig line
Stoutland (face and beard only)
Pansear
Swoobat (borderline gold)
The Timburr line
The Tympole line (vibrators only; only really orange on Palpitoad)
Cottonee
Dwebble
Scraggy
The Archen line (face and tail only)
Autumn Deerling and all Sawsbuck
Emolga (borderline brown)
The Larvesta line
Landorus (borderline gold)
Hoopa (borderline gold and brown)
The Litten line
The Mudbray line
The Morelull line
Passimian (head and fruit only)
Pyukumuku (top parts only)
Drampa
The Jangmo-o line (borderline gold)
Guzzlord (mouth only)
The Poiple line
Stakataka
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